Question

Draw a circle of diameter $10$cm. From a point P, $13$cm away from its centre, draw the two tangents PA and PB to the circle, and measure their lengths.

Answer 1

$Step1:$ With $O$ as the center draw a circle of radius $5cm$.

$Step2:$ Mark a point $P$ at a distance of $13cm$ from $O$ and join $OP$.

$Step3:$ Draw the perpendicular bisector of $OP$. Let it meet $OP$ at $M.$

$Step4:$ With $M$ as center and $MO$ as radius, draw another circle.

$Step5:$ Let the two circles intersect at $X$ and $Y$.

$Step6:$ Join $PX$ and $PY$. They are required tangents.

Thus, this is the resulting figure.

To determine the length of the tangent, consider the triangle $OXP$ and apply Pythagoras theorem to it:

$O{X}^2+P{X}^2=O{P}^2$

$5^2+P{X}^2={13}^2$

$P{X}^2=169–25$

$P{X}^2=144$

$PX=12cm$

Thus, the length of the tangents is $12cm$.